The founders of quantum mechanics all realized that RELATIVITY posits a linear relationship between energy and momentum of a massive particle, while NONRELATIVISTIC classical mechanics, which is a mere approximation, implies that kinetic energy is related to the square of the momentum. Since light always moves at light speed, the approximate treatment does not apply to photons.
The founders always explained whether they were working relativistically or approximately, so there was never a mistake or a confusion on that score. But there were plenty of different mistakes and confusions in their work -- some surviving to this day. Hans Christian von Baeyer
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